The waiting time at a bus station can be modeled as a continuous random variable T in units of minutes. The random variable is statistically described by its probability density t/3 Os153/2 function f, (t) given by fr (1) ={-(t / 5) +4/5 3/2s154. a) Verify that f, (1) as given is otherwise a) define the event B= {T > 1} . Obtain the conditional probability density function f;(t / B) of the random variable T and verify that the solution proposed is indeed a valid probability density function. b) Based on the information given in Problem a, define the event B = {T > 1} . Obtain the conditional cdf F, (t / B) and verify that the solution proposed is indeed a valid probability density function. Plot this conditional cdf (use MATLAB). c) Based on the work in Problem b, determine the conditional mean E{T / B} and the
The waiting time at a bus station can be modeled as a continuous random variable T in units of minutes. The random variable is statistically described by its probability density t/3 Os153/2 function f, (t) given by fr (1) ={-(t / 5) +4/5 3/2s154. a) Verify that f, (1) as given is otherwise a) define the event B= {T > 1} . Obtain the conditional probability density function f;(t / B) of the random variable T and verify that the solution proposed is indeed a valid probability density function. b) Based on the information given in Problem a, define the event B = {T > 1} . Obtain the conditional cdf F, (t / B) and verify that the solution proposed is indeed a valid probability density function. Plot this conditional cdf (use MATLAB). c) Based on the work in Problem b, determine the conditional mean E{T / B} and the
A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Transcribed Image Text:The waiting time at a bus station can be modeled as a continuous random variable T in
units of minutes. The random variable is statistically described by its probability density
t/3
OsI33/2
function f, () given by f, (1) ={-(t / 5) +4/5 3/2s154. a) Verify that f, (1) as given is
otherwise
a) define the event B= {T >1} . Obtain the
conditional probability density function f;(t / B) of the random variable T and verify that
the solution proposed is indeed a valid probability density function.
b) Based on the information given in Problem a, define the event B = {T > 1} . Obtain the
conditional cdf F, (t / B) and verify that the solution proposed is indeed a valid probability
density function. Plot this conditional cdf (use MATLAB).
c) Based on the work in Problem b, determine the conditional mean E{T / B} and the
conditional variance var{T / B} of the random variable T.
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